Verification Complexity and Extension of Classical Shadows

arXiv:2609.40107 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Verifier — 35× in this paper · explained in 2 episodes
• Trace — 29× in this paper · explained in 2 episodes
• Consistency — 25× in this paper · explained in 3 episodes
• Verification — 21× in this paper · explained in 2 episodes
• BQP — 7× in this paper · explained in 2 episodes
• Hilbert Space — 6× in this paper · explained in 2 episodes
• Classical Shadow Validity — 5× in this paper
• Regularization — 5× in this paper · explained in 3 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Decode — 4× in this paper · explained in 2 episodes
• Trace Distance — 4× in this paper · explained in 3 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Shadow Tomography — 3× in this paper · explained in 4 episodes
• Quantum Circuits — 2× in this paper · explained in 2 episodes
• Aggregation — 1× in this paper · explained in 1 episode
• Ancilla Qubits — 1× in this paper · explained in 1 episode
• Annual Symposium on Foundations of Computer Science — 1× in this paper
• Combinatorial Optimization — 1× in this paper · explained in 2 episodes
• Generative AI — 1× in this paper · explained in 2 episodes
• Hypergraph — 1× in this paper · explained in 2 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes

Sources

• The Quantum Schur Transform: I. Efficient Qudit Circuits
• Perfect zero knowledge for quantum multiprover interactive proofs
• On the Complexity of Pure-State Consistency of Local Density Matrices
• Classical shadows with symmetries
• Quantum Computational Complexity

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